Positive mass theorem in extended supergravities

TL;DR

This paper extends the positive mass theorem to various extended supergravity theories using a Weyl spinor formalism, identifying conditions under which mass positivity holds, including for complex scalar systems and gauged supergravity.

Contribution

It generalizes the positive mass theorem to extended supergravities by classifying gauge connection conditions ensuring positivity, applicable to multiple supergravity models.

Findings

Positivity conditions are satisfied in several supergravity theories.

Mass positivity holds for Einstein-scalar systems with Hodge-Kahler target space.

Mass positivity in N=8 gauged supergravity is independent of gaugings and deformations.

Abstract

Following the Witten-Nester formalism, we present a useful prescription using Weyl spinors towards the positivity of mass. As a generalization of arXiv:1310.1663, we show that some "positivity conditions" must be imposed upon the gauge connections appearing in the supercovariant derivative acting on spinors. A complete classification of the connection fulfilling the positivity conditions is given. It turns out that these positivity conditions are indeed satisfied for a number of extended supergravity theories. It is shown that the positivity property holds for the Einstein-complex scalar system, provided that the target space is Hodge-Kahler and the potential is expressed in terms of the superpotential. In the Einstein-Maxwell-dilaton theory with a dilaton potential, the dilaton coupling function and the superpotential are fixed by the positive mass property. We also explore the $N=8$ gauged supergravity and demonstrate that the positivity of the mass holds independently of the gaugings and the deformation parameters.